The use of continuous boundary elements in the boundary elements method for domains with non-smooth boundaries via finite difference approach

A numerical method is presented in this article to deal with the drawback of boundary elements method (BEM) at corner points. The use of continuous elements instead of the discontinuous ones has been recommended in the BEM literature widely because of the simplicity and accuracy. However the continuous elements lead to certain difficulties for problems where their domains contain corners. In this paper the finite difference method (FDM) has been applied to obtain some constraints for boundary points near the corners to deal with this drawback. Because of its simplicity and capability, the new scheme is applicable on BEM problems for all geometries, all governing equations and general boundary conditions, easily. Since the Dirichlet boundary condition is more critical than the other ones, we will focus on it in the numerical implementation. The numerical results show that the new treatment improves the accuracy of BEM significantly.